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September 24, 2014

C 2014 American Chemical Society

Quantitative Angle-ResolvedSmall-Spot Reflectance Measurementson Plasmonic Perfect Absorbers:Impedance Matching and DisorderEffectsAndreas Tittl,*,† Moshe G. Harats,‡ Ramon Walter,† Xinghui Yin,† Martin Schaferling,† Na Liu,§

Ronen Rapaport,‡ and Harald Giessen†

†4th Physics Institute and Research Center SCOPE, University of Stuttgart, D-70569 Stuttgart, Germany, ‡The Racah Institute of Physics and the Applied PhysicsDepartment, The Hebrew University of Jerusalem, Jerusalem, Israel, and §Max Planck Institute for Intelligent Systems, D-70569 Stuttgart, Germany

Plasmonic absorbers incorporate reso-nant particles above a dielectric spacerlayer and metallic mirror to achieve

absorbance close to unity in a variety ofspectral ranges. Starting from original ex-periments in the gigahertz and terahertzregions,1,2 plasmonic and metamaterial-based perfect absorbers havemoved towardthe near-infrared and visible spectral ranges,with applications ranging from glucose andgas sensing to spectroscopy and photovol-taic efficiency enhancement.3�6 To extendthe concept of plasmonic perfect absorptiontoward technological applications, opticalelements with high acceptance angles arerequired. Such elements are able to absorbmost radiation from the incidence half-space,enabling improved sensitivity and efficiencyin a wide range of devices.7�16 However,so far, detailed experimental studies on the

underlying reason for the angular dispersionof plasmonic perfect absorbers at visibleand near-infrared wavelengths are missing.This is associated with the fact that angle-resolved reflectance measurements withquantitative accuracy, especially in the infra-red spectral range, are not easily performed,particularly in common FTIR microscopysetups. Samples where only small areashave been nanostructured, for example,by electron-beam lithography, pose furtherchallenges.In this paper, we use a simple and elegant

k-space measurement approach to recordlarge-angle and polarization-dependent re-flectance measurements on different per-fect absorber geometries. Combining theseresultswith extensivenumericalmodeling,wedevelop and verify a quantitative model forthe angular behavior of plasmonic absorbers.

* Address correspondence toa.tittl@pi4.uni-stuttgart.de.

Received for review August 21, 2014and accepted September 24, 2014.

Published online10.1021/nn504708t

ABSTRACT Plasmonic devices with absorbance close to unity have emerged as

essential building blocks for a multitude of technological applications ranging

from trace gas detection to infrared imaging. A crucial requirement for such

elements is the angle independence of the absorptive performance. In this work,

we develop theoretically and verify experimentally a quantitative model for the

angular behavior of plasmonic perfect absorber structures based on an optical

impedance matching picture. To achieve this, we utilize a simple and elegant

k-space measurement technique to record quantitative angle-resolved reflectance measurements on various perfect absorber structures. Particularly, this

method allows quantitative reflectance measurements on samples where only small areas have been nanostructured, for example, by electron-beam

lithography. Combining these results with extensive numerical modeling, we find that matching of both the real and imaginary parts of the optical

impedance is crucial to obtain perfect absorption over a large angular range. Furthermore, we successfully apply our model to the angular dispersion of

perfect absorber geometries with disordered plasmonic elements as a favorable alternative to current array-based designs.

KEYWORDS: plasmonics . perfect absorbers . angular dispersion . impedance matching

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In particular, we determine the imaginary part of theoptical impedance in our plasmonic absorbers to bethe key factor for angle-independent performance.One key advantage of our experimental method isthe ability to measure the angular response of plas-monic samples with small structured areas, making itideally suited for the investigation of nanoscale devicesfabricated using electron-beam lithography.To shed light on the angular absorptive performance

of our systems, we examine the angle-dependentreflectance from four different perfect absorber de-signs in p-polarization (Figure 1a,b). The experimentalsetup is depicted in Figure 1c.The perfect absorber sample is illuminated (red

beam), and the corresponding reflected beam (lightred beam) is collected by the objective. The back focalplane (which constitutes the Fourier plane17) of theobjective is imagedonto the entrance slit of a spectrom-eter mounted with a Princeton Instruments PIXISCCD (in the visible spectral range) or OMA V array (inthe infrared). Using the spectrometer adds the abilityto analyze the spectral response alongwith the angularresponse of the system.The polar angles θ,j are related to the k-space

(Fourier plane) by the following relation:

kB ¼ kxxþ kyy ¼ 2πλ

sinθ cosj xþ 2πλ

sin θ sinj y

In this work, the measurement setup is aligned atj = 0�, with the polarization parallel to the incident

plane, as shown in Figure 1a, so only the polar angle θ isresolved. In the case of samples in the visible range, theCCD camera resolves the full spectral-angular responseof the sample in one single measurement. Generally,the angular range of this measurement is only limitedby the numerical aperture of the objective. In the caseof samples in the NIR spectral range, the OMA V arrayrecords the spectral response only for a specific angle.Therefore, amotorized stage is used to scan the imagedFourier plane on the spectrometer slit to resolve the fullangular response of the perfect absorber.This spectral-angular k-space imaging technique is

easy to implement and very powerful for measuringsmall-area plasmonic structures efficiently and withhigh precision.18 In our case, when using samplesnanostructured by electron-beam lithography, onlya 100 μm � 100 μm area is measured. We note that,in most previous works, the optical response of perfectabsorbers was commonly shown only for normal in-cidence, and no full angular characterization wasdemonstrated experimentally. Additionally, perfectabsorbers are usually measured using a goniometricapproach, which requires tilting the detectors, thesamples, or both. This approach is very sensitive toalignment errors, and since each angle is measuredseparately, it requires very long measurement times.Also, typical goniometric reflection setups in commer-cial ellipsometers have minimum beam sizes in themillimeter range, making them unsuitable for measur-ing small-area plasmonic structures. The angular reso-lution is also limited by the mechanical steps of thegoniometric stage. With the spectral-angular k-spaceimaging technique, we can resolve the spectral-angularresponse of small-area samples without any alignmenterrors, with high spectral and angular resolution, andwith a very fast measurement.

RESULTS AND DISCUSSION

As a first demonstration of our method, we examinea well-known near-infrared perfect absorber designconsisting of an array of gold nanodisks stacked abovea magnesium fluoride (MgF2) spacer layer and a Aumirror.3 In the original work, an absorbance of 99%wasexperimentally demonstrated at normal incidence.However, the angular dispersion was only investigatedusing numerical simulations.The full angular dispersion of this perfect absorber

design in a wide angular range from �36 to 36�(limited by the numerical aperture of the objective) isshown in Figure 2a for a structure with a disk diameterof 330 nm, a disk height of 20 nm, a periodicity of600 nm, a spacer height of 30 nm, and a mirror heightof 200 nm.We observe a clear reflectance dip at a wavelength

of 1480 nm, with a minimum reflectance of around 2%and reflectance values below 10% over the wholeangular range. Thus, we experimentally verify, for the

Figure 1. System under investigation. (a) Schematic of theangle-dependent reflectancemeasurements discussed in thiswork. We can study the optical response for incident lightparallel and perpendicular to the plane of incidence (p- ands-polarization). (b) Overview of the four investigated plasmo-nic perfect absorber structures. (c) Schematic drawing of thespectral-angular k-space experimental setup used to obtainquantitative large-angle reflectance measurements from ourstructures. The back focal plane of the lens, which is theFourier plane of the illuminated sample, is imaged onto theentry slit of a spectrometer to obtain reflectance spectra for alarge range of incident angles simultaneously.

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first time, the near angle independence of this perfectabsorber design.To support our measurements theoretically, we per-

form numerical simulations using a scattering-matrix-based Fourier modal method19,20 (Figure 2b; for simu-lation details, see the Methods section). We find anexcellent agreement between simulation and experi-ment, with a pronounced reflectance dip again at aresonance wavelength of 1480 nm. The angle inde-pendence over the full range is also well-reproduced.Still, we find a somewhat broader spectral response ofthe resonance in the experiment when compared tothe simulations. This is most likely due to inhomoge-neous broadening as well as additional grain bound-aries introduced during the nanostructuring of the Audisks.The performance and especially the angular disper-

sion of perfect absorbers can be well-understood byconsidering an optical impedancematching picture. Ingeneral, a reflectance of zero in an optical element canbe obtained by matching is optical impedance Z to thevalue of the surrounding space. In perfect absorbers,this impedance can be tuned by varying geometricparameters such as the size of the resonant structureor the thickness of the spacer layer. Since the thickmetallic mirror below the structure ensures zero trans-mittance, perfect impedance matching consequentlyresults in perfect absorption at a certain designwavelength.The underlying physics behind perfect absorption

are commonly explained in one of two ways. The firstexplanation assumes resonant near-field coupling be-tween the top nanostructure and the metallic mirrorbelow. Thus, when light impinges on the structure,particle plasmon oscillations are excited in the resonantstructure on top. The corresponding charge distributionthen causes the oscillation of a mirror plasmon in thethick metallic film below. By tuning the thicknessof the dielectric spacer layer, the phase delay betweenthe plasmon and the mirror plasmon oscillation can beadjusted so they oscillate in antiphase. This is assumed

to lead to the formation of a circular current distribu-tion and consequently an induced magnetic modein the spacer layer, which enables control over theimpedance, and can also be found in other plasmonicgeometries.21,22 Additionally, impedance matchingplays an important role in areas such as plasmonwaveguiding.23

Recently, it has been shown that the near-fieldinteraction of the resonant particle and the mirrorcan be decoupled, and the absorptive behavior canbe explained in terms of interference between thetwo layers.24 However, we stress that, regardless ofthe microscopic explanation of the perfect absorptionbehavior, the impedance matching model for the fulloptical element remains valid.The impedance of our structure can be calculated

easily from the scattering parameter results of ournumerical simulations, using

Z ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(1þ S11)

2 � S221(1 � S11)

2 � S221

s(1)

where S11 and S21 denote the scattering matrix coeffi-cients of normal incidence reflection and transmissionin p-polarization, respectively. Due to the presence ofthe thick metallic mirror, S21 can safely be set to zero.It is important to note that Z = Z0 þ i 3 Z

00 is, in general,a complex value.Figure 3 shows the simulation results for the real and

imaginary parts of the optical impedance comparedto the reflectance for the Au disk array-based perfectabsorber. We can clearly observe that both the realand the imaginary parts are perfectly matched to therespective vacuum values of one and zero (in cgs units)at resonance, resulting in angle-independent perfectabsorption.In nanostructured plasmonic absorber arrays, the

main reason for a lack of angle independence is a

Figure 3. Numerical calculation of the reflectance andoptical impedance of the Au disk array perfect absorberfrom Figure 2 at normal incidence. Both the real andimaginary parts of the optical impedance are perfectlymatched to the vacuum values of one and zero, resultingin angle-independent perfect absorption.

Figure 2. (a) Spectral-angular reflectance measurements ofthe near-infrared Au-based perfect absorber. (b) Numericalsimulation of the same system. The color bar represents thereflectance with perfect absorption corresponding to zeroreflectance (blue).

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coupling of the absorber resonance to the first diffrac-tion order associated with the grating periodicity ofthe array. For a given incident angle θ, this Rayleighanomaly appears at wavelengths given by

λR ¼ p(nenv þ sin θ) (2)

where p is the periodicity of the array and nenv is therefractive index of the surrounding medium or thespacer layer, respectively. The presence of the Rayleighanomaly introduces additional impedance, causinga loss of the perfect impedance matching andthus reduced absorption.25�27 Consequently, the de-sign of angle-independent perfect absorber structuresrequires sufficiently small periodicities to ensure ade-quate spectral separation between the particle plas-mon mode and the Rayleigh anomaly for all requiredincident angles θ. In this way, interaction between thegrating mode and the perfect absorber resonance canbe suppressed, leading to angle-independent absor-bance. The spectral separation condition is neatlyfulfilled in the Au absorber case. For a periodicity ofp= 600 nm, and considering the interface of the spacerlayer (MgF2, n = 1.38), the Rayleigh anomaly is foundat λR = 830 nm, which is well away from the perfectabsorber resonance at λ0 = 1480 nm.However, the concept of spectral separation between

Rayleigh anomaly and perfect absorber resonance doesnot allow to judge, in a quantitative way, whether agiven perfect absorber design is angle-independent ornot. In the following,wewill show that perfectmatchingof the imaginary part of the impedance is crucial toobtain fully angle-independent perfect absorption. Toprove the reliability of this model, we will now focus onthe more challenging concept of a perfect absorber inthe visible wavelength range. To elucidate the influenceof the grating mode, we compare two palladium-basedperfect absorbers with different periodicities. In bothcases, the designs consist of Pd wires stacked abovea dielectric spacer and a Au mirror that ensures zerotransmission.4 Figure 4a shows the spectral-angularreflectance measurements of a Pd-based perfect absor-ber with a periodicity of 450 nm, awire width of 100 nm,a wire height of 20 nm, a MgF2 spacer height of 65 nm,and a mirror thickness of 200 nm. Even though theabsorbance reaches amaximumof 95%at awavelengthof 720 nm at normal incidence, we observe a strongangular dispersion when moving to higher incidentangles. Consequently, this design can only be used upto an acceptance angle of θ = (14� while maintainingan absorbance of A > 90%. This result is again well-supported by our numerical simulations (Figure 4b).The angular optical response of a Pd-based perfect

absorber with a smaller periodicity of 300 nm, a wirewidth of 85 nm, a wire height of 30 nm, an Al2O2 spacerheight of 35 nm, and a mirror thickness of 200 nmis shown in Figure 4c. For this optimized geometry,the angular dispersion is greatly reduced. The small

periodicity design again offers very high absorbance of98% at a wavelength of 690 nm and maintains absor-bance A > 90% for acceptance angles up to θ = (36�.This constitutes an increase of the acceptance angleby close to a factor of 2.5 over the absorber with largerperiodicity, which is again in excellent agreement withour simulations (Figure 4d).The optical impedance matching model now allows

quantification of the influence of gratingmodes on theangular behavior of the perfect absorber resonance.For the large periodicity case (p = 450 nm, Figure 5a),only the real part of the optical impedance is perfectlymatched to one, which ensures zero reflectance atnormal incidence. However, there is pronounced mis-match of ΔZ00 = �0.2 in the imaginary part of theimpedance (in cgs units). This indicates the presenceof a grating mode close to the resonance, which causesthe strong angular dispersion. The fact that the reflec-tance at normal incidence is near zero despite theimpedancemismatch canbeunderstood by calculatingthe reflectance as a function of the complex impedanceZ = Z0 þ i 3 Z

00. Assuming near-perfect matching of thereal part of the impedance (Z0 =1) and a smallmismatchof the imaginary part (|Z00| , 1), this yields

R ¼ (Z 0� 1)2 þ (Z 00)2

(Z 0þ1)2 þ (Z 00)2� (Z 00)2

4� 0 (3)

Consequently, a small impedance mismatch of theimaginary part has only a negligible influence on the

Figure 4. (a) Spectral-angular reflectance measurementson a Pd-based perfect absorber in the visible wavelengthrange. The periodicity is p = 450 nm. (b) Numerical simula-tion of the same system. (c) Spectral-angular reflectancemeasurements on a Pd-basedperfect absorber in the visiblewavelength range. The periodicity is p = 300 nm. Note thegreatly reduced angle dependence due to the smallerperiodicity. (d) Numerical simulation of the same system.

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reflectance at normal incidence. When moving tolarger angles, however, thismismatchquickly increases,leading to the observed strong angular dispersion(Supporting Information Figure S1).In contrast, for the small periodicity case (p= 300 nm),

both the real and the imaginary parts of the impedanceare perfectly matched to the respective vacuum valuesof one and zero, resulting in “true” angle-independentperfect absorption (Figure 5b).To further examine the transition from small to large

periodicities, we examine a continuous transition fromthe p = 300 nm to the p = 450 nm case. To achieve this,we consider the small periodicity design from Figure 4cand only introduce a gradual increase of the periodicity(Figure 6).The real part of the optical impedance remains close

to one for the whole periodicity range, while theimaginary part deviates strongly, reaching a maximumimpedance mismatch of ΔZ00 = �0.6 for the largestperiodicity of 450 nm. Thus, even though the absor-bance at normal incidence of this system remains veryhigh (A > 92%) for increasing periodicity, the angular

behavior is strongly modified. This proves that theimaginary part of the optical impedance is a reliabledesign parameter and quantitative indicator for theangle independence of array-based plasmonic perfectabsorber geometries. Thus, an array-based perfectabsorber design which exhibits R = 0 at normal in-cidence as well as Z00 = 0will not be strongly influencedby grating effects and should consequently providethe highest possible acceptance angles and, for mostapplications, the best performance.One intriguing alternative approach for obtaining

angle-independent perfect absorbers is a systemwherethe plasmonic resonators are placed on the spacer layerin a disordered fashion rather than in an array. However,the numerical design and optimization of such struc-tures is challenging due to the very large computationaldomains associated with disordered systems. Con-sequently, we start our numerical design process withan array-based sample and optimize the geometry toobtain perfect absorption at the desired resonancewavelength. A disordered geometry with a similar sur-face coverage is then realized experimentally usingcolloidal nanofabrication. For such disordered samples,our measurement method enables high-throughputcharacterization of the angular response of such struc-tures at a wide range of operating wavelengths.Figure 7a shows spectral-angular reflectance mea-

surement of a disordered Au-based perfect absorberwith a disk diameter of 160 nm, a disk height of 20 nm,a MgF2 spacer height of 40 nm, and a mirror thicknessof 120 nm. Importantly, this Au-based absorber worksin the red part of the visible spectral range, wherethe design of angle-independent perfect absorbers ischallenging. The disordered Au nanodisks were pro-duced using colloidal etching lithography (see SEMimage in Figure 7b; fabrication details can be found inthe Methods section).In this system, we observe a high absorbance of

A=92%at awavelengthof 780nm for normal incidence,which remains above 90% for acceptance angles up to

Figure 5. Numerical calculation of the reflectance and op-tical impedance of the two previously discussed Pd-basedplasmonic perfect absorbers. (a) For a large periodicity of p=450 nm, only the real part of the impedance is perfectlymatched. The mismatch in the imaginary part indicates thepresence of propagating modes and thus leads to strongerangle dependence of the absorption. (a) For a small periodi-city of p = 300 nm, both the real and imaginary parts of theoptical impedance are perfectly matched to the vacuumvalues, resulting in angle-independent perfect absorption.

Figure 6. Impedance at resonance and at normal incidenceof a Pd-based perfect absorber for increasing periodicity.The real part of the impedance remains mostly constant,while the imaginary part moves away from the vacuumvalue of zero for larger periodicities.

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θ = (36�. The performance of the disordered designcan be understood in terms of our impedance match-ing model by considering two determining factors:the local impedance matching of individual absorberelements and the suppression of interparticle couplingand grating effects via their spatial arrangement.To first examine the local impedance matching,

we calculate the optical impedance of an individualperfect absorber element consisting of one Au nano-disk stacked above aMgF2 spacer layer and aAumirror.This simulation is carried out using a FDTD approach(calculation details are provided in the Methodssection). The results of this simulation are shown inFigure 7c.We find a distinct reflectanceminimum closeto the experimental resonance position, as well asperfect matching of the real and imaginary parts ofthe optical impedance to vacuum values of one andzero. Thus, when considered separate from possiblegrating contributions, our design should exhibit excel-lent angle-independent performance.Regarding the spatial arrangement of the individual

absorber elements, there are two crucial requirementsfor angle independence: The interparticle distanceneeds to be large enough to prevent near-field couplingof adjacent resonators, and the spatial arrangement ofthe particles needs to deviate sufficiently from an exactarray to suppress the formation of gratingmodes. In oursample, the Au nanodisks form a disordered structurewith a surface coverage of approximately 25%, whichcorresponds to a half-pitch grating in the array case.

To further quantify the particle distribution in oursample, we extract the locations of all nanodisks fromthe SEM image and find a median interparticle distanceof around 345 nm with a standard deviation of 140 nm(Figure 7d). Considering the strong decay of plasmonicnear-fields on the order of several tens of nanometers,this yields mostly uncoupled single plasmonic absorberstructures.28,29 Together with the fabrication-induceddisorder, the significant spread of interparticle distances(which constitute different available periodicities) inthe system leads to an effective suppression of gratingeffects.30 Thus, the perfect impedance matching ofindividual perfect absorber elements combined witha suppression of the grating contribution yields fullyangle-independent performance.

CONCLUSION

We have developed and verified a quantitativemodel for the angular behavior of plasmonic perfectabsorber structures based on the optical impedancepicture. Using high-throughput angle-resolved reflec-tance measurements and numerical simulations,we have found that it is crucial to match both the realand imaginary parts of the optical impedance tovacuum values to obtain “true” angle-independentperfect absorption. We identified the imaginary partof the impedance as a reliable design parameter andquantitative indicator for the angle independenceof plasmonic perfect absorber geometries. Our modelwas successfully verified for both array-based and

Figure 7. (a) Spectral-angular reflectance measurements on a disordered Au-based perfect absorber in the 800 nmwavelength range. (b) SEM image of the disordered absorber structure. (c) Simulated reflectance and optical impedanceof an individualAudiskperfect absorber element. Both the real and the imaginaryparts of theoptical impedance are perfectlymatched to the vacuum values of one and zero. (d) Histogram of the median interparticle distances extracted from the SEMimage in b. We find a median distance of around 345 nm with a standard deviation of 140 nm. Due to the disorder and thespread of available periodicities, grating effects are effectively suppressed.

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disordered perfect absorber geometries in the visibleand near-infrared spectral ranges and can be easilyextended toward other resonance wavelengths. Theinsights gained from our impedance model enable the

rapid design of angle-independent plasmonic perfectabsorber geometries and will lead to a multitude ofapplications of absorbing elements with high accep-tance angles in the future.

METHODSAngle-Dependent Numerical Simulations. Numerical simula-

tions for the four perfect absorber geometries were performedusing a scattering-matrix-based Fourier modal method.19,20

All structures were defined on a glass substrate (n = 1.5). Thearray-based Au perfect absorber consisted of Au nanodisks(diameter = 320 nm, periodicity = 600 nm, height = 20 nm)placed above a MgF2 spacer layer (thickness = 30 nm, n = 1.38)and a Au mirror (thickness = 200 nm). Optical constants for Auwere taken from the literature.31 The palladium-based perfectabsorber design with large periodicity consisted of a Pd wiregrating (wirewidth=125nm, periodicity = 450nm,wire height =20 nm) placed above a MgF2 spacer layer (thickness = 50 nm)and a Au mirror (thickness = 200 nm). Optical constants for Pdwere again taken from the literature.32 The palladium-basedperfect absorber with small periodicity consisted of a Pd wiregrating (wire width = 85 nm, periodicity = 300 nm, wire height =30 nm) placed above a Al2O3 spacer layer (thickness = 35 nm,n = 1.75) and a Au mirror (thickness = 200 nm).

Impedance Calculation for Individual Absorber Elements. The im-pedances for the randomly arranged perfect absorber werecalculated in Lumerical FDTD solutions. To this end, a singleparticle calculation employing a cubic 450 nm total-field-scat-tered field source containing the complete absorber geometry(120 nm Au mirror, 40 nm MgF2 spacer, and one Au disk witha diameter of 160 nm and a height of 20 nm) was carried out.The entire FDTD simulation domain spanned a 5 μm side lengthcube bounded by perfectly matched layers. The boundaries ofthe scattered-field region, which coincided with the boundariesof the simulation domain, were chosen such that the fieldsat the Au mirror were already sufficiently decayed to ensurethe convergence of the simulation. This isolated the absorptiveperformance of a single absorber element. The impedance ex-tracted from this simulationwas equivalent to the impedance ofa surface covered with noninteracting absorber elements of anaverage density of at least 1/(450 nm)2, effectively excludinggrating effects. The amplitude and phase of a normal incidencebackward-scattered wave were extracted. In order to obtain thescattering matrix parameter S11 from this, we corrected for thepropagation phase from the source to the absorber and back tothe monitor. The impedance was then calculated according toZ = [(1 þ S11)

2/(1 � S11)2]1/2.

Fabrication of the Perfect Absorber Samples. The array-basedperfect absorber designs were fabricated as described pre-viously.3,4 The disordered Au-based perfect absorber designwas fabricated using a colloidalmethod. Starting froma cleanedborosilicate substrate, all necessary materials were evaporatedusing electron-beam-assisted deposition. The deposited materi-al system consisted of a 5 nm titanium adhesion layer, a 120 nmAumirror, a 50 nmMgF2 spacer layer, followedby another 20 nmof Au and a 40 nm Ni sacrificial layer.

The Ni surface was treated in an O2 plasma for 18 s, and asolution of PDDA was drop-coated. Next, the sample was rinsedwith demineralized water and dried with N2. Directly after thisstep, PS nanospheres (160 nm diameter, nonfunctionalized,0.2 wt % in water, ultrasoniced for about 40 min) were drop-coated on the surface, rinsed after 1 min with demineralizedwater, and immersed in hot water (98 �C) for about 3 min. Afterthis, the sample was dried with N2. To produce the nanodisks,the sample was then dry etched with an Ar ion beam for 300 s.The PS nanospheres were removed by putting the sample inacetone for about 12 h, followed by treatment in O2 plasmafor 30 min. The sample was put in diluted (1:9) sulfuric acidfor 2 min, rinsed afterward with demineralized water, and driedwith N2.

Calculation of Interparticle Distances in the Disordered Perfect Absor-ber. Statistics on the interparticle distances in the disorderedperfect absorber geometry were calculated using a customMATLAB script. First, the locations of the individual nanodiskswere extracted from the SEM image in Figure 7b using MA-TLAB's image processing toolbox. To add a neighbor relation-ship to the data set, a Delaunay triangulation was created forthe array of nanodisk positions. The interparticle distance wasthen defined as the average distance of each nanodisk from itsneighbors in the triangulation. This definition is a good repre-sentation of the effective particle separation and thus usefulfor the estimation of grating contributions in our impedancemodel.

Conflict of Interest: The authors declare no competingfinancial interest.

Acknowledgment. We are grateful to D. Dregely andR. Taubert for providing the Pd-based perfect absorber samplesinvestigated in this study. We thank T. Weiss for help withthe numerical simulations. A.T., R.W., X.Y., M.S., and H.G. werefinancially supported by the Deutsche Forschungsgemeinschaft(SPP1391, FOR730, GI 269/11-1), the Bundesministerium fürBildung und Forschung (13N9048 and 13N10146), the ERCAdvanced Grant COMPLEXPLAS, the Baden-Württemberg Stif-tung (Spitzenforschung II), and theMinisterium fürWissenschaft,Forschung und Kunst Baden-Württemberg (Az: 7533-7-11.6-8).X.Y. additionally acknowledges support by the Carl-Zeiss-Stiftung. M.H. and R.R. acknowledge financial support bythe FIRST Program of the Israel Science Foundation (Grant No.1046/10). Financial support by the European Cooperation inScience and Technology through COST Action MP1302 Nano-spectroscopy is gratefully acknowledged. We acknowledgefunding through the German�Israel Foundation (GIF) and theAlexander-von-Humboldt Foundation.

Supporting Information Available: Numerical simulationsof the angle-dependent optical impedance, Figure S1.This material is available free of charge via the Internet athttp://pubs.acs.org.

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